Krylov Subspace Acceleration Method for Nonlinear Multigrid Schemes
نویسنده
چکیده
In this paper we present a Krylov acceleration technique for nonlinear PDEs. As a `precon-ditioner' we use nonlinear multigrid schemes, like FAS 1]. The beneets of the combination of nonlinear multigrid and the new proposed accelerator is shown for diicult nonlinear ellip-tic scalar problems, like the Bratu problem and for systems of nonlinear equations, like the Navier-Stokes equations.
منابع مشابه
Krylov Subspace Acceleration for Nonlinear Multigrid Schemes∗
In this paper we present a Krylov acceleration technique for nonlinear PDEs. As a ‘preconditioner’ we use nonlinear multigrid schemes such as the Full Approximation Scheme (FAS) [1]. The benefits of nonlinear multigrid used in combination with the new accelerator are illustrated by difficult nonlinear elliptic scalar problems, such as the Bratu problem, and for systems of nonlinear equations, s...
متن کاملKrylov Subspace Acceleration of Nonlinear Multigrid with Application to Recirculating Flows
This paper deals with the combination of two solution methods: multigrid and GMRES [SIAM J. Sci. Comput., 14 (1993), pp. 856–869]. The generality and parallelizability of this combination are established by applying it to systems of nonlinear PDEs. As the “preconditioner” for a nonlinear Krylov subspace method, we use the full approximation storage (FAS) scheme [Math. Comp., 31 (1977), pp. 333–...
متن کاملAcceleration Methods for Total Variation-Based Image Denoising
For a given blur, we apply a fixed point method to solve the total variation-based image restoration problem. A new algorithm for the discretized system is presented. Convergence of outer iteration is efficiently improved by adding a linear term on both sides of the system of nonlinear equations. In inner iteration, an algebraic multigrid (AMG) method is applied to solve the linearized systems ...
متن کاملOn a Multilevel Krylov Method for the Helmholtz Equation Preconditioned by Shifted Laplacian
In Erlangga and Nabben [SIAM J. Sci. Comput., 30 (2008), pp. 1572–1595], a multilevel Krylov method is proposed to solve linear systems with symmetric and nonsymmetric matrices of coefficients. This multilevel method is based on an operator which shifts some small eigenvalues to the largest eigenvalue, leading to a spectrum which is favorable for convergence acceleration of a Krylov subspace me...
متن کاملMixed-Precision GPU-Multigrid Solvers with Strong Smoothers
• Sparse iterative linear solvers are the most important building block in (implicit) schemes for PDE problems • In FD, FV and FE discretisations • Lots of research on GPUs so far for Krylov subspace methods, ADI approaches and multigrid • But: Limited to simple preconditioners and smoothing operators •Numerically strong smoothers exhibit inherently sequential data dependencies (impossible to p...
متن کامل